A Speedy Algorithm for Estimating the Correlation Dimension.

A new modified Grassberger and Precaccia Algorithm (GPA), called Δr neighborhood GPA, is investigated to estimate the correlation dimension (D[sub 2]) in this paper. Comparison of time cost between the new algorithm and other GPAs exhibits its efficiency with scaling as O(N * N[sub ref]/q[sup 2]), whereas the original algorithm's is O(N[sup 2]), the box-assisted correlation algorithm's is O(Nlog N). The D[sub 2] result of Lorenz model calculated by the new algorithm satisfies the expectation well and thus tests its accuracy. Finally, a theoretical evaluation of the time cost of the Δr neighborhood GPA is discussed. [ABSTRACT FROM AUTHOR]